hiro/arb
1
0
Fork 0
mirror of https://github.com/vale981/arb synced 2025-03-06 01:41:39 -05:00
Code Issues Projects Releases Packages Wiki Activity Actions

documentation update

Browse source
This commit is contained in:
Fredrik Johansson 2013-07-30 15:26:41 +02:00
parent d6ef6f70b2
commit a2129ba203
1 changed files with 16 additions and 9 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

25
doc/source/gamma.rst
View file

@ -90,18 +90,25 @@ Evaluation using the Stirling series
.. math ::
\log \Gamma(z) - R(n,z) = \left(z-\frac{1}{2}\right)\log z - z +
\frac{\ln {2 \pi}}{2} + \sum_{k=1}^{n-1} t_k
where
.. math ::
t_k = \frac{B_{2k}}{2k(2k-1)z^{2k-1}}.
\log \Gamma(z) = \left(z-\frac{1}{2}\right)\log z - z +
\frac{\ln {2 \pi}}{2}
+ \sum_{k=1}^{n-1} \frac{B_{2k}}{2k(2k-1)z^{2k-1}}
+ R(n,z).
If *digamma* is nonzero, the derivative of this series (i.e. the
expansion for the digamma function) is evaluated.
The error bound for the tail `R(n,z)` is included in the output.
The error bound for the tail `R(n,z)` (computed via
:func:`gamma_stirling_bound_fmprb` or
:func:`gamma_stirling_bound_fmpcb`) is included in the output.
.. function :: void gamma_stirling_eval_fmprb_series(fmprb_ptr res, const fmprb_t z, long n, long num, long prec)
.. function :: void gamma_stirling_eval_fmpcb_series(fmpcb_ptr res, const fmpcb_t z, long n, long num, long prec)
Evaluates the Stirling series of a power series `z + t`,
computing *num* coefficients. The error bound (computed via
:func:`gamma_stirling_bound_fmprb` or
:func:`gamma_stirling_bound_fmpcb`) is included in the output.
.. function :: void gamma_stirling_bound_phase(fmpr_t bound, const fmpcb_t z, long prec)